Problem: $A$ $B$ $C$ If: $ AB = 4x + 5$, $ AC = 22$, and $ BC = 5x + 8$, Find $BC$.
Explanation: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {4x + 5} + {5x + 8} = {22}$ Combine like terms: $ 9x + 13 = {22}$ Subtract $13$ from both sides: $ 9x = 9$ Divide both sides by $9$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $BC$ $ BC = 5({1}) + 8$ Simplify: $ {BC = 5 + 8}$ Simplify to find ${BC}$ : $ {BC = 13}$